“A form of portfolio risk that arises when the possibility that an investment will move more than three standard deviations from the mean is greater than what is shown by a normal distribution”

and

“Tail risk is sometimes defined less strictly, as merely the risk (or probability) of rare events”

So, expanding on the points from Th.M and jmh, I would say that tail risks encompass far more than unknown unknowns. Those are a component of tail risk, but it also encompasses events that could be foreseen but are viewed as extremely low probability (3 standard deviations is a 0.03% probability of occurring). Call them “knowns viewed as more improbable than they actually are.”

I agree that by the time people are thinking about an event as having a 25% chance of happening, it is no longer a tail risk.

]]>By: Th.Mhttp://blogs.reuters.com/felix-salmon/2013/01/28/you-keep-using-that-word-i-do-not-think-it-means-what-you-think-it-means/comment-page-1/#comment-45683
Mon, 28 Jan 2013 17:06:12 +0000https://blogs.reuters.com/felix-salmon/?p=20319#comment-45683A bit of both, maybe. There is no precedent for exiting the Euro, but there are some for sovereign default, and “tail risk” might refer to the last one.
]]>By: jmh530http://blogs.reuters.com/felix-salmon/2013/01/28/you-keep-using-that-word-i-do-not-think-it-means-what-you-think-it-means/comment-page-1/#comment-45682
Mon, 28 Jan 2013 15:36:01 +0000https://blogs.reuters.com/felix-salmon/?p=20319#comment-45682I was going to echo what Th.M was going to say, but I think there is an issue of phrasing. For instance, I can take S&P500 returns and fit a t or stable distribution and obtain Conditional Value at Risk (CVaR) to measure tail risk. However, what these policy makers are talking about isn’t tail risk in the sense of measured CVaR. They are basically talking about black swans or Knightian uncertainty. They know that the probability of a Greek default scenario has declined, even if they cannot formulate the distribution of securities prices in the event that it would occur.
]]>By: klhoughtonhttp://blogs.reuters.com/felix-salmon/2013/01/28/you-keep-using-that-word-i-do-not-think-it-means-what-you-think-it-means/comment-page-1/#comment-45681
Mon, 28 Jan 2013 14:55:51 +0000https://blogs.reuters.com/felix-salmon/?p=20319#comment-45681I will not type “tail risk was eliminated from the EU when DSK was replaced by Christine Lagarde.”

A year ago, a Grexit went from being tail risk to being mainstreamed. Now, Cyprus and Portugal have joined Greece, while Draghi pretends that countries with 20%+ unemployment (Eire, Latvia) are “recovered.”

The “tail risk” right now is that people will realise that the combination of risks that have been mainstreamed means that German banks are insolvent. Fortunately, no one will ever realise that.

I don’t know whose definition you are using but there is a whole branch of statistical literature (Extreme Value Theory) devoted to measuring tail risks. It originated in the study of (I think) floods, and is routinely used in insurance, finance etc.

]]>By: GRRRhttp://blogs.reuters.com/felix-salmon/2013/01/28/you-keep-using-that-word-i-do-not-think-it-means-what-you-think-it-means/comment-page-1/#comment-45679
Mon, 28 Jan 2013 12:06:27 +0000https://blogs.reuters.com/felix-salmon/?p=20319#comment-45679Oddly enough, Donald Rumsfeld made the best quote regarding tail risk:
“As we know, there are known knowns: There are things we know we know.
We also know there are known unknowns: That is to say we know there are some things we do not know.
But there are also unknown unknowns: The ones we don’t know we don’t know.”

At the time, it just seemed nonsensical on the surface, but like a Mickey Mantle quote, it quite simply tells you exactly what you need to know.

Tail Risks and Fat Tails do not have to be “unknown unknowns”, they are just outcomes that indicate a severely non-normal distribution of outcomes, so that people who are used to stability or are caught unprepared. Something that is widely discussed, like Greece leaving the euro, is a legitimate tail risk as a result of its low generally assumed probability, even if its fallout cannot be precisely calibrated, which is what makes it a “known unknown”. Martian invasion is also a tail risk, one that cannot seriously be contemplated in any kind of scenario planning.

To illustrate: let’s play a card game where you pay $1 per draw, but if you get dealt the ace of spades you win $52. The expected value of a single draw is zero, but you almost always lose; the standard deviation is $7.2 which makes drawing the ace of spades a 7-standard-deviation event. It is the tail risk.

Now, if we modify the game so that you don’t shuffle after every draw, and after playing a while there are two cards left, one of which is the ace of spades, I’d agree that it is no longer a tail risk event. But even while a few people thought a Grexit was likely, it was never the markets’ view that the outcome had a high likelihood, except perhaps for a few weeks in mid-2012.

]]>By: winstongatorhttp://blogs.reuters.com/felix-salmon/2013/01/28/you-keep-using-that-word-i-do-not-think-it-means-what-you-think-it-means/comment-page-1/#comment-45676
Mon, 28 Jan 2013 11:28:42 +0000https://blogs.reuters.com/felix-salmon/?p=20319#comment-45676Tail risk has different meanings in different contexts. In the medical community, it refers to the risk of litigation after you have stopped practicing, or have switched jobs – times where your normal malpractice insurance would have changed.

I think Draghi is using tail risk to refer to risks that arose that were unforeseen. In that case, the problems in Greece, Spain and Ireland should not be viewed as tail risk, but the cost of the monetary union. Hoocoudanode?

If he is merely taking about an asset price moving more than 3 standard deviations from its mean, he is using the term correctly. He can keep Greece’s bond prices within 3 std-dev’s from their mean, especially now since their volatility has dramatically increased their sigma. However, there are problems in addition to merely Greece’s bond prices.

Normal distributions are ridiculous in some situations. First, most asset price movements are bounded by 0. That stock you bought can go to zero, but not below. However, it could go from 10 to 10,000. You will have a hard time capturing that behavior in a normal distribution. Yes, law of large numbers, blah, the risk being measured is the price of a single asset.

Bond prices are also somewhat limited on the high end. Who would pay $10,000 for a bond with $10 par value (and not a collector’s item). You could think of interest rate movements that could generate that, but you’d have to start out at a very high rate. However, a lot of complicated math has been built upon the foundation of the Gaussian distribution. Undoing the use in instances where the Gaussian does not tether to real events would be a positive.